Methods of manufacturing polyresistors with selected tcr

ABSTRACT

Various embodiments provide computer program products and computer implemented methods. In some embodiments, aspects provide for a method of manufacturing a polysilicon resistor with a selected temperature coefficient of resistance (TCR), the method including selecting a sheet resistance for the polysilicon resistor, the selected sheet resistance being related to a selected film thickness of the polysilicon resistor, selecting a dose level for a grain size modulating species (GSMS) for modulating an average grain size of grains of the polysilicon resistor, selecting a thermal coefficient of resistance (TCR) for the polysilicon resistor, the TCR being related to a selected average grain size of the polysilicon and forming the polysilicon resistor on a substrate, the polysilicon resistor having the selected sheet resistance, the selected GSMS dose level and the selected TCR.

FIELD

The subject matter disclosed herein relates generally to resistors. Moreparticularly, the subject matter disclosed relates to measuring thetemperature coefficient of resistance (TCR) for resistors and methods ofmanufacturing resistors with a controlled thermal coefficient ofresistance.

BACKGROUND

In general, polysilicon resistors are created to have a specific sheetresistance or a range of sheet resistances. Currently, polysiliconresistors and resistors of other materials are created usingmanufacturing processes that target a given sheet resistance andtherefore dope the polysilicon at targeted doping levels with suitablemasks. Such manufacturing approaches do not generally control for thethermal behavior(s) of the resistors so manufactured and, therefore,resistors created using such methods generally exhibit greater or lesserresistance as ambient or operating temperature changes. Generally, thischange in resistance due to temperature changes can be described by athermal coefficient of resistance (TCR). A positive TCR indicates changein resistance and change in temperature being proportional to oneanother, while a negative TCR indicates inverse proportionality, i.e., aresistor that exhibits increased resistance when operating temperaturerises has a positive TCR, and a resistor that exhibits loweredresistance as operating temperature rises has a negative TCR. Also, aresistor that does not exhibit changes in resistance due to changes inoperating temperature has a zero TCR.

BRIEF DESCRIPTION

Various aspects of the invention provide for a method of manufacturing apolysilicon resistor with a selected temperature coefficient ofresistance (TCR), the method including selecting a sheet resistance forthe polysilicon resistor, the selected sheet resistance being related toa selected film thickness of the polysilicon resistor, selecting a doselevel for a grain size modulating species (GSMS) for modulating anaverage grain size of grains of the polysilicon resistor, selecting athermal coefficient of resistance (TCR) for the polysilicon resistor,the TCR being related to a selected average grain size of thepolysilicon and forming the polysilicon resistor on a substrate, thepolysilicon resistor having the selected sheet resistance, the selectedGSMS dose level and the selected TCR.

A first aspect provides a method of manufacturing a polysilicon resistorwith a selected temperature coefficient of resistance (TCR), the methodcomprising: selecting a sheet resistance for the polysilicon resistor,the selected sheet resistance being related to a selected film thicknessof the polysilicon resistor; selecting a dose level for a grain sizemodulating species (GSMS) for modulating an average grain size of grainsof the polysilicon resistor; selecting a thermal coefficient ofresistance (TCR) for the polysilicon resistor, the TCR being related toa selected average grain size of the polysilicon; and forming thepolysilicon resistor on a substrate, the polysilicon resistor having theselected sheet resistance, the selected GSMS dose level and the selectedTCR.

A second aspect provides a computer-implemented method for calculating atemperature coefficient of resistance (TCR) for a polysilicon resistoron a substrate using at least one computing device, the methodcomprising: measuring a density of states (DOS) for traps within thepolysilicon resistor using one of deep level transient spectroscopy(DLTS), the polysilicon resistor having a selected sheet resistance thatis related to a selected polysilicon film thickness and a selected doselevel for a grain size modulating species (GSMS) for modulating anaverage grain size of grains of the polysilicon resistor; creating atechnology computer aided design (TCAD) model of the polysiliconresistor by performing a TCAD simulation on the polysilicon resistor;matching the TCAD model with a measured current versus voltagecharacteristic for the polysilicon resistor; calculating a resistanceversus voltage characteristic based on the measured current versusvoltage characteristic for the polysilicon resistor; converting theresistance versus voltage characteristic to a resistance versustemperature characteristic using the TCAD simulation model; andcalculating the TCR for the polysilicon resistor using the resistanceversus temperature characteristic.

A third aspect provides a computer program product comprising programcode stored on a computer-readable storage medium, which when executedby at least one computing device, enables the at least one computingdevice to implement a method of calculating a temperature coefficient ofresistance (TCR) for a polysilicon resistor by performing actionsincluding: creating a technology computer aided design (TCAD) model of apolysilicon resistor by performing a TCAD simulation on the polysiliconresistor, wherein the polysilicon resistor has a selected sheetresistance that is related to a selected polysilicon film thickness anda selected dose level for a grain size modulating species (GSMS), theGSMS for modulating an average grain size of grains of the polysiliconresistor, wherein the polysilicon resistor has a measured current versusvoltage characteristic, and wherein the polysilicon resistor has ameasured density of states (DOS) for traps within the polysiliconresistor; matching the TCAD model with a measured current versus voltagecharacteristic for the polysilicon resistor; calculating a resistanceversus voltage characteristic based on the measured current versusvoltage characteristic for the polysilicon resistor; converting theresistance versus voltage characteristic to a resistance versustemperature characteristic using the TCAD simulation model; andcalculating the TCR for the polysilicon resistor using the resistanceversus temperature characteristic

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features of this invention will be more readilyunderstood from the following detailed description of the variousaspects of the invention taken in conjunction with the accompanyingdrawings that depict various embodiments of the invention, in which:

FIG. 1 shows a flow diagram illustrating a method according to variousembodiments.

FIG. 2 shows a flow diagram illustrating a method according to variousembodiments.

FIG. 3A shows a graph illustrating measured and simulated data accordingto embodiments.

FIG. 3B shows a graph illustrating measured and simulated data accordingto embodiments.

FIG. 4 shows a graph illustrating data according to embodiments.

FIG. 5 shows an illustrative environment according to variousembodiments.

FIG. 6 shows an illustrative polysilicon resistor structure according tovarious embodiments.

It is noted that the drawings of the invention are not necessarily toscale. The drawings are intended to depict only typical aspects of theinvention, and therefore should not be considered as limiting the scopeof the invention. In the drawings, like numbering represents likeelements between the drawings.

DETAILED DESCRIPTION

The subject matter disclosed herein relates generally to resistors. Moreparticularly, the subject matter disclosed relates to measuring thetemperature coefficient of resistance (TCR) for resistors and methods ofmanufacturing resistors with a controlled thermal coefficient ofresistance.

As discussed above, polysilicon resistors are generally created with aspecific sheet resistance or a range of sheet resistances in mind andtheir methods of manufacture do not generally control for thermalbehavior. For many applications, it may be problematic to use resistorscreated using such methods because ambient or operating temperaturechanges can cause the resistors to exhibit uncontrolled resistiveproperties.

Embodiments described herein include methods of measuring temperaturecoefficient of resistance (TCR) for polysilicon resistors and methodsfor the manufacture of polysilicon resistors with a desired TCR. Whilecurrent manufacturing processes target a given sheet resistance byapplying dopants with a suitable masks and do not control the thermalbehavior of the polysilicon resistor, resistors made according toembodiments described herein exhibit controlled TCRs. According toembodiments, polysilicon resistors with fine-tuned, or even zero TCRsmay be valuable devices for use in circuit design where thermaldegradation (i.e., change in resistance) could negatively impact circuitbehavior.

Under normal processing conditions polysilicon consists of many grainswith variable sizes, mostly influenced by the process parametersincluding deposition process, anneal temperature and anneal duration. Todate, grain-engineering has not been used in systematic applications fordevice design and development. Controlled grain growth, in itself, is ademanding and difficult-to-implement process. Embodiments describedherein combine grain-control with a detailed TCAD simulation setup intomethodologies that feed/supplement the technology development process tooptimize the production of almost zero TCR polysilicon resistors fordemanding analog applications. The ability to produce a zero TCRresistor or a combination of resistors with selected TCRs is of immensevalue to the design community, as this ability allows designers toachieve temperature-independent electrical behavior in designed devices.The TCAD method of calculating TCR is novel. However, when it comes tothe manufacturing steps the TCR may be measured either via the novelTCAD method (as described herein) or via a plurality of experiments,although the TCAD method may be more feasible in terms of time andresources required. TCR values obtained by performing a first of the twomethods may be validated by performing the second method to re-obtainthose TCR values. During manufacturing processes, calculating the TCRmay be performed either by adopting the above novel TCAD method or byperforming a plurality of experiments. Applications for suchTCR-controlled resistors include, but are not limited to currentmirrors.

Turning now to FIG. 1, a flow diagram is shown illustrating processesthat may be performed in a method according to various embodiments. FIG.1 illustrates a method for calculating a temperature coefficient ofresistance (TCR) for a polysilicon resistor. Process P100 includesforming the polysilicon resistor on a substrate, the polysiliconresistor having a selected sheet resistance that is related to aselected film thickness and a selected doping level for the polysiliconresistor. In general, such resistors are made on a wafer with standardmaterials, and of thicknesses that corresponds to appropriate sheetresistances, using standard doping methods. Such polysilicon resistorshaving selected sheet resistances may be created using any now known orlater developed method or process. It should be noted that a polysiliconresistor having a selected sheet resistance may be simply acquired, andaccording to some embodiments, the actual creation of the resistor maynot be necessary.

After creation of the polysilicon resistor in process P100, or theacquisition of a resistor having a selected sheet resistance, processP110 may be performed. Process P110 includes measuring a density statefor traps within the polysilicon resistor using deep level transientspectroscopy (DLTS). It should be noted that DLTS is a suitable methodto measure the density of states but one could measure resistances andTCR and simply tune the density of states (DOS) in the TCAD to match theresistances and TCR, and such tuning may be performed according toembodiments of the inventive concepts. It should be further noted thatDLTS may be used to measure the depopulation of trap states as atransient capacitance response to a periodic injection of carriers as afunction of injection frequency and temperature and from this density ofstates can be calculated and such processes may be performed accordingto embodiments.

Process P120 includes creating a technology computer aided design (TCAD)model of the polysilicon resistor by performing a TCAD simulation on thepolysilicon resistor. TCAD analysis allows for the inputting ofmaterials properties and parameters and dopant properties. Inputs intothe TCAD model include, but are not limited to the physical structure ofthe device, dopant type(s), dopant concentration(s) and the DOS.Further, process P120 may include fine tuning model parameters such astrap physics, self-heating models, emission and absorption ratecoefficients at the traps, mobility models etc., to obtain a good matchbetween the TCAD and the observed resistance and temperature coefficientof resistance. The resistance and TCR may be extracted from a singlevoltage sweep which includes a high enough voltage to induceself-heating in the resistor, or from multiple low voltage sweeps atmultiple temperatures. The TCAD model is used to supply simulatedtemperature, as shown in FIG. 3B, discussed below. Thus, the TCR may bedetermined by either of the two methods. First, by resistancemeasurements at few temperature points, second, by employing the TCADmodel. Once the TCR is so determined the next step of modifying thegrain sizes using grain size modulating species may be employed to finetune the process towards the desired/targeted TCR. As discussed above,the TCR may be measured either via the novel TCAD method (as describedherein) or via a plurality of experiments, although the TCAD method maybe more feasible in terms of time and resources required. TCR valuesobtained by performing a first of the two methods may be validated byperforming the second method to re-obtain those TCR values. Theelectro-thermal impact of using a different combination of GSMS doselevel and composition may be determined by several “what if” scenariosusing the TCAD model, e.g. if the TCR has not reached its target, thenpolysilicon grain size may be changed in a TCAD model and if TCR iscalculated to be closer to the target, then the new grain size may beused in a fabricated wafer. I.e., in this example, once the new grainsize is determined, then a new GSMS dose may be determined. The GSMSdose level may include a concentration of the GSMS and a composition ofthe GSMS.

FIG. 2A illustrates resistance versus voltage curves interpolated frommeasured current vs. voltage data. The illustrated data was taken frompolysilicon resistors using ten different voltages at four differentsites on a single wafer. Illustrative resistance vs. voltage curves areshown in FIG. 3A and are discussed above. Converting a current vs.voltage to a resistance vs. voltage curve may be performed using Ohm'slaw and no special equipment should be necessary to make suchcalculations, however such calculations may be performed using acomputing device with an appropriate processor and appropriateprogramming. One curve showing simulated data from a TCAD model createdfrom inputted parameters related to the physical wafer is also shown. Ascan be seen in FIG. 3A, the simulated data tracks well with the measureddata and its interpolated curves.

Continuing with the method illustrated in FIG. 1, P130 includescalculating a resistance versus voltage characteristic based on ameasured current versus voltage characteristic for the polysiliconresistor and P140 includes converting the resistance versus voltagecharacteristic to a resistance versus temperature characteristic usingthe TCAD simulation model. The TCAD model is used to simulate atemperature vs. normalized resistance curve, as illustrated in FIG. 3Bas discussed above.

Moving on, process P150 includes calculating the TCR for the polysiliconresistor using the resistance versus temperature characteristic. ProcessP150 may be performed, for example by reading the simulated temperatureof the device for any given voltage bias and calculating the slope of aresulting resistance vs. temperature plot. Process P150 is performedusing the TCAD simulation model discussed above, and an illustrative TCRcurve is shown in FIG. 3B. The TCR is a coefficient that relatestemperature to resistance for a given polysilicon resistor. According toaspects, calculating the TCR may be performed either by adopting theabove novel TCAD method or by a plurality of experiments. FIG. 4illustrates five illustrative curves for five different resistors havingfive different TCRs. Three of the illustrated TCRs are positive and twoare negative. The illustrated TCR curves each correspond to apolysilicon grain size and therefore to a specific trap density statefor a given polysilicon grain size distribution Note that the curves arelinear over the temperature ranges shown. It should be further notedthat the displayed resistances are normalized to a value of 1. That is,in this illustrative example, the data has been normalized with the roomtemperature resistance of each of the resistors for a proper comparisonof the slopes and highlighting the changing TCR with polysilicon grainsize. The resistance of these resistors changes as operating temperaturechanges, as discussed above. While not shown in FIG. 4, it is possibleto have a TCR of zero, in which case, the resistance would remain at thenormalized value of 1 as temperature changes. Such a zero TCR resistoror a combination of resistors with selected TCRs allows for fabricationof devices having temperature-independent electrical behavior.

Referring back to FIG. 1, FIG. 1 illustrates process P160 which includesdetermining whether the calculated TCR complies with a target TCR. Ifthe calculated TCR complies with a target TCR, then process P160 may bea stopping point according to embodiments. However, if the calculatedTCR does not comply with a target TCR, the further processes may beperformed as illustrated. Process P170 may be performed in response tothe calculated TCR not complying with the target TCR. Process P170includes forming of the polysilicon resistor using an adjusted dose ofthe grain size modulating species (GSMS) different from the selecteddose. It should be understood that a dose of the grain size modulatingspecies includes a concentration and composition of the grain sizemodulating species In performing process P170, the resistance vs.temperature characteristic may serve as a reference. Also theinformation gained in process P150 may be added to a growing database ofsuch information. Adjusting the dose of the grain size modulatingspecies (GSMS) is understood to mean that dose of the GSMS is adjustedrelative to the selected dose of the GSMS. According to someembodiments, the selected doping level may include an averagepolysilicon grain size, while the adjusted dose of the GSMS may resultin a greater average polysilicon grain size than the polysilicon grainsize of the selected dose level of the GSMS. Alternatively, the adjusteddose level of the GSMS may include a lesser average concentration andcomposition of the GSMS, than the grain size of the selected GSMS doselevel. Also according to embodiments, the greater average polysilicongrain size and/or the lesser average polysilicon grain size may beestimated using the TCAD simulation model, furthermore, TCAD may be usedto simulate any of several other materials and electrical parameters andproperties. After performing optional process P170, processes P110,P120, P130, P140 and P150 may be repeated, as illustrated in FIG. 1.This loop may be reiterated until the TCR calculated in process P150complies with a target TCR as discussed above with respect to FIG. 1.Also after performing process P170, data such as polysilicon grain sizeand TCR may be added to the database discussed above with respect toprocess P150.

FIG. 2 illustrates a flow diagram is shown illustrating processes thatmay be performed in a method according to various embodiments. FIG. 2illustrates a method of manufacturing a polysilicon resistor with aselected temperature coefficient of resistance (TCR). Process P200includes selecting a sheet resistance for the polysilicon resistor, theselected sheet resistance being related to a selected film thickness ofthe polysilicon resistor. As discussed above with respect to processP100, the polysilicon resistor may be manufactured or acquired with theselected sheet resistance. Process P210 includes selecting a dose levelfor a grain size modulating species (GSMS) for modulating an averagegrain size of grains of the polysilicon resistor. Process P220 includesselecting a thermal coefficient of resistance (TCR) for the polysiliconresistor, the TCR being related to a selected average grain size of thepolysilicon and process P240 includes forming the polysilicon resistoron a substrate, the polysilicon resistor having the selected sheetresistance, the selected GSMS dose level and the selected TCR. The orderof performing processes P200, P210 and P220 may not be important. I.e.,process P220 may be performed before or after either of processes P200and P210. The order of processes P200, P210 and P220 is illustrated insuch an order only for the sake of explanation. Also, the selection ofsheet resistance, the GSMS dose level and the selection of TCR aredescribed above with respect to processes P100-P170 and will not berepeated for the sake of brevity.

Embodiments may include creating a look-up table by recording, in adatabase, each calculated TCR along with their associated GSMS doselevel. The look up table may be useful for future creation ofpolysilicon resistors. That is, the look up table may be used to avoidrepeating some or all of the iterative steps described above because thegrain size used in a first resistor may be appropriate for a target TCR.The dose level recorded in the look up table may include a concentrationof the GSMS and a composition of the GSMS.

Turning now to FIG. 5, an illustrative environment according to variousembodiments is shown. FIG. 5 depicts an illustrative environment 100 forproviding a computer system for calculating a temperature coefficient ofresistance (TCR) for a polysilicon resistor. To this extent, theenvironment 100 includes a computer system 102 that can perform aprocess described herein in order to calculate a TCR for a polysiliconresistor. In particular, the computer system 102 is shown as including aTCAD simulation program 130 and a TCR calculation program 135, whichmake computer system 102 operable to handle all necessary calculationsand functions by performing any/all of the processes described hereinand implementing any/all of the embodiments described herein. While TCADsimulation program 130 and TCR calculation program are illustratedwithin storage component 106, it should be understood that programs 130and 135 may be stored separately on different storage components, andthat parts of each program may be stored on different storagecomponents.

Computer system 102 is shown including a processing component 104 (e.g.,one or more processors), a storage component 106 (e.g., a storagehierarchy), an input/output (I/O) component 108 (e.g., one or more I/Ointerfaces and/or devices), and a communications pathway 110. Ingeneral, the processing component 104 executes program code, such asTCAD simulation program 130 or TCR calculation program 135, both ofwhich may be at least partially fixed in the storage component 106.While executing program code, the processing component 104 can processdata, which can result in reading and/or writing transformed datafrom/to the storage component 106 and/or the I/O component 108 forfurther processing. The pathway 110 provides a communications linkbetween each of the components in the computer system 102. The I/Ocomponent 108 can comprise one or more human-directed, ornon-human-directed I/O devices, which enable a user 112 to interact withthe computer system 102 and/or one or more communications devices toenable a system user 112 to communicate with the computer system 102using any type of communications link. User 112 may be a human,including a technician, or a non-human system. Both TCAD simulationprogram 130 and TCR calculation program 135 can manage a set ofinterfaces (e.g., graphical user interface(s), application programinterface, etc.) that enable human and/or system users 112 to interactwith TCAD simulation program 130 and TCR calculation program 135.Further, the TCAD simulation program 130 and TCR calculation program 135can each manage (e.g., store, retrieve, create, manipulate, organize,present, etc.) data, such as data 142, etc., using any solution.

In any event, computer system 102 can comprise one or more generalpurpose computing articles of manufacture (e.g., computing devices)capable of executing program code, such as TCAD simulation program 130and TCR calculation program 135, installed thereon. As used herein, itis understood that “program code” means any collection of instructions,in any language, code or notation, that cause a computing device havingan information processing capability to perform a particular functioneither directly or after any combination of the following: (a)conversion to another language, code or notation; (b) reproduction in adifferent material form; and/or (c) decompression. To this extent, TCADsimulation program 130 and TCR calculation program 135 can be embodiedas any combination of system software and/or application software.

Further, the TCAD simulation program 130 and TCR calculation program 135can be implemented using a set of modules 132. In this case, a module132 can enable the computer system 102 to perform a set of tasks used byTCAD simulation program 130 and TCR calculation program 135, and can beseparately developed and/or implemented apart from other portions ofTCAD simulation program 130 and TCR calculation program 135. As usedherein, with reference to the computer system hardware, the term“component” means any configuration of hardware, with or withoutsoftware, which implements the functionality described in conjunctiontherewith using any solution, while the term “module” means program codethat enables the computer system 102 to implement the functionalitydescribed in conjunction therewith using any solution. When fixed in astorage component 106 of a computer system 102 that includes aprocessing component 104, a module is a substantial portion of acomponent that implements the functionality. Regardless, it isunderstood that two or more components, modules, and/or systems mayshare some/all of their respective hardware and/or software. Further, itis understood that some of the functionality discussed herein may not beimplemented or additional functionality may be included as part of thecomputer system 102.

When the computer system 102 comprises multiple computing devices, eachcomputing device may have only a portion of TCAD simulation program 130and TCR calculation program 135 fixed thereon (e.g., one or more modules132). However, it is understood that the computer system 102 and TCADsimulation program 130 and TCR calculation program 135 are onlyrepresentative of various possible equivalent computer systems that mayperform a process described herein. To this extent, in otherembodiments, the functionality provided by computer system 102 and TCADsimulation program 130 and TCR calculation program 135 can be at leastpartially implemented by one or more computing devices that include anycombination of general and/or specific purpose hardware with or withoutprogram code. In each embodiment, the hardware and program code, ifincluded, can be created using standard engineering and programmingtechniques, respectively.

When computer system 102 includes multiple computing devices, thecomputing devices can communicate over any type of communications link.Further, while performing a process described herein, computer system102 can communicate with one or more other computer systems using anytype of communications link. In either case, the communications link cancomprise any combination of various types of wired and/or wirelesslinks; comprise any combination of one or more types of networks; and/orutilize any combination of various types of transmission techniques andprotocols.

Computer system 102 can obtain or provide data, such as data 142 usingany solution. For example, computer system 102 can generate and/or beused to generate data 142, retrieve data 142, from one or more datastores, receive data 142, from another system, send data 142 to anothersystem, etc.

While shown and described herein as methods for calculating a TCR for apolysilicon resistor, it is understood that aspects of the inventionfurther provide various alternative embodiments. For example, in oneembodiment, the invention provides a computer program fixed in at leastone computer-readable medium, which when executed, enables a computersystem to perform a method of calculating a TCR for a polysiliconresistor. To this extent, the computer-readable medium includes programcode, such as TCAD simulation program 130 and TCR calculation program135, which implement some or all of a process described herein. It isunderstood that the term “computer-readable medium” comprises one ormore of any type of tangible medium of expression, now known or laterdeveloped, from which a copy of the program code can be perceived,reproduced, or otherwise communicated by a computing device. Forexample, the computer-readable medium can comprise: one or more portablestorage articles of manufacture; one or more memory/storage componentsof a computing device; paper; and/or the like.

In another embodiment, the invention provides a method of providing acopy of program code, which implements some or all of a processdescribed herein. In this case, a computer system can process a copy ofprogram code that implements some or all of a process described hereinto generate and transmit, for reception at a second, distinct location,a set of data signals that has one or more of its characteristics setand/or changed in such a manner as to encode a copy of the program codein the set of data signals. Similarly, an embodiment of the inventionprovides a method of acquiring a copy of program code that implementssome or all of a process described herein, which includes a computersystem receiving the set of data signals described herein, andtranslating the set of data signals into a copy of the computer programfixed in at least one computer-readable medium. In either case, the setof data signals can be transmitted/received using any type ofcommunications link.

In still another embodiment, the invention provides a method ofcalculating a TCR for a polysilicon resistor. In this case, a computersystem, such as computer system 102 (FIG. 5), can be obtained (e.g.,created, maintained, made available, etc.) and one or more componentsfor performing a process described herein can be obtained (e.g.,created, purchased, used, modified, etc.) and deployed to the computersystem. To this extent, the deployment can comprise one or more of: (1)installing program code on a computing device; (2) adding one or morecomputing and/or I/O devices to the computer system; (3) incorporatingand/or modifying the computer system to enable it to perform a processdescribed herein; and/or the like.

It is understood that aspects of the invention can be implemented aspart of a business method that performs a process described herein on asubscription, advertising, and/or fee basis. That is, a service providercould offer to characterize an optical mask as described herein. In thiscase, the service provider can manage (e.g., create, maintain, support,etc.) a computer system, such as computer system 102 (FIG. 5), thatperforms a process described herein for one or more customers. Inreturn, the service provider can receive payment from the customer(s)under a subscription and/or fee agreement, receive payment from the saleof advertising to one or more third parties, and/or the like.

Turning now to FIG. 6, an illustrative polysilicon resistor structure200 according to various embodiments is shown. Polysilicon resistorstructure 200 is shown having substrate 210 and polysilicon resistorbody 220. Polysilicon resistor body includes polysilicon grains 225 andgrain size modulating species (GSMS) 230 interspersed betweenpolysilicon grains 225. Substrate 210 may be chosen from any appropriatematerial including, but not limited to silicon oxide, another insulatingmaterial or any other appropriate material or materials for givenpurpose. Polysilicon grains 225 and GSMS 230 are discussed herein aboveand descriptions of grains 225 and GSMS 230 will not be repeated for thesake of brevity.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof.

This written description uses examples to disclose the invention,including the best mode, and also to enable any person skilled in theart to practice the invention, including making and using any devices orsystems and performing any incorporated methods. The patentable scope ofthe invention is defined by the claims, and may include other examplesthat occur to those skilled in the art. Such other examples are intendedto be within the scope of the claims if they have structural elementsthat do not differ from the literal language of the claims, or if theyinclude equivalent structural elements with insubstantial differencesfrom the literal languages of the claims.

What is claimed is:
 1. A method of manufacturing a polysilicon resistor with a selected temperature coefficient of resistance (TCR), the method comprising: selecting a sheet resistance for the polysilicon resistor, the selected sheet resistance being related to a selected film thickness of the polysilicon resistor; selecting a dose level for a grain size modulating species (GSMS) for modulating an average grain size of grains of the polysilicon resistor; selecting a thermal coefficient of resistance (TCR) for the polysilicon resistor, the TCR being related to a selected average grain size of the polysilicon; and forming the polysilicon resistor on a substrate, the polysilicon resistor having the selected sheet resistance, the selected GSMS dose level and the selected TCR.
 2. The method of claim 1, further comprising: measuring a density of states (DOS) for traps within the polysilicon resistor using deep level transit spectroscopy (DLTS); creating a technology computer aided design (TCAD) model of the polysilicon resistor by performing a TCAD simulation on the polysilicon resistor; calculating a resistance versus voltage characteristic based on a measured current versus voltage characteristic for the polysilicon resistor; converting the resistance versus voltage characteristic to a resistance versus temperature characteristic using the TCAD simulation model; and calculating the TCR for the polysilicon resistor by using the resistance versus temperature characteristic.
 3. The method of claim 2, further comprising: determining whether the calculated TCR complies with a target TCR; and in response to the calculated TCR not complying with the target TCR: repeating the forming of the polysilicon resistor using the resistance versus temperature characteristic as a reference and selecting a new GSMS dose level, the new GSMS dose level being related to a desired polysilicon grain size to achieve the target TCR, the measuring of the density state for traps for the new dose level of the GSMS the creating of the TCAD model, the calculating of the resistance versus voltage characteristic, the converting of the resistance versus voltage characteristic, and the calculating of the TCR, wherein the repeated forming of the polysilicon resistor includes using an adjusted dose level for the GSMS different from the selected dose level.
 4. The method of claim 3, wherein the selected dose level is related to an average polysilicon grain size and wherein the adjusted dose level is related to a greater average polysilicon grain size than the selected dose level.
 5. The method of claim 3, further comprising: estimating the greater average polysilicon grain size using the TCAD simulation model.
 6. The method of claim 3, wherein the selected dose level is related to an average polysilicon grain size and wherein the adjusted dose level is related to a lesser average polysilicon grain size than the selected dose level.
 7. The method of claim 6, further comprising: estimating the lesser average polysilicon grain size using the TCAD simulation model.
 8. The method of claim 2, further comprising: creating a look-up table by recording, in a database, each calculated TCR and each GSMS dose level associated with each calculated TCR, wherein each dose level includes a concentration of the GSMS and a composition of the GSMS.
 9. A computer-implemented method for calculating a temperature coefficient of resistance (TCR) for a polysilicon resistor on a substrate using at least one computing device, the method comprising: measuring a density of states (DOS) for traps within the polysilicon resistor using one of deep level transient spectroscopy (DLTS), the polysilicon resistor having a selected sheet resistance that is related to a selected polysilicon film thickness and a selected dose level for a grain size modulating species (GSMS) for modulating an average grain size of grains of the polysilicon resistor; creating a technology computer aided design (TCAD) model of the polysilicon resistor by performing a TCAD simulation on the polysilicon resistor; matching the TCAD model with a measured current versus voltage characteristic for the polysilicon resistor; calculating a resistance versus voltage characteristic based on the measured current versus voltage characteristic for the polysilicon resistor; converting the resistance versus voltage characteristic to a resistance versus temperature characteristic using the TCAD simulation model; and calculating the TCR for the polysilicon resistor using the resistance versus temperature characteristic.
 10. The method of claim 9, wherein the at least one computing device is further configured to perform actions including: determining whether the calculated TCR complies with a target TCR; and in the case that the calculated TCR does not comply with the target TCR; repeating the measuring of the DOS for traps, the creating of the TCAD model, the matching of the TCAD model with the measured current versus voltage characteristic, the calculating of the resistance versus voltage characteristic, the converting of the resistance versus voltage characteristic, and the calculating of the TCR, wherein the repeated measuring of the current versus voltage characteristic includes using a polysilicon resistor with an adjusted GSMS dose level, different from the selected dose level.
 11. The method of claim 10, wherein the selected dose level is related to an average polysilicon grain size and wherein the adjusted dose level is related to a greater average polysilicon grain size than the selected dose level.
 12. The method of claim 11, further comprising: estimating the greater average polysilicon grain size using the TCAD simulation model.
 13. The method of claim 10, wherein the selected dose level is related to an average polysilicon grain size and wherein the adjusted dose level is related to a lesser average polysilicon grain size than the selected dose level.
 14. The method of claim 13, further comprising: estimating the lesser average polysilicon grain size using the TCAD simulation model.
 15. The method of claim 9, wherein the at least one computing device is further configured to perform actions including: creating a look-up table by recording, in a database, each calculated TCR and each dose level of the GSMS associated with each calculated TCR, wherein each dose level includes a level of the GSMS and a composition of the GSMS.
 16. A computer program product comprising program code stored on a computer-readable storage medium, which when executed by at least one computing device, enables the at least one computing device to implement a method of calculating a temperature coefficient of resistance (TCR) for a polysilicon resistor by performing actions including: creating a technology computer aided design (TCAD) model of a polysilicon resistor by performing a TCAD simulation on the polysilicon resistor, wherein the polysilicon resistor has a selected sheet resistance that is related to a selected polysilicon film thickness and a selected dose level for a grain size modulating species (GSMS), the GSMS for modulating an average grain size of grains of the polysilicon resistor, wherein the polysilicon resistor has a measured current versus voltage characteristic, and wherein the polysilicon resistor has a measured density of states (DOS) for traps within the polysilicon resistor; matching the TCAD model with a measured current versus voltage characteristic for the polysilicon resistor; calculating a resistance versus voltage characteristic based on the measured current versus voltage characteristic for the polysilicon resistor; converting the resistance versus voltage characteristic to a resistance versus temperature characteristic using the TCAD simulation model; and calculating the TCR for the polysilicon resistor using the resistance versus temperature characteristic.
 17. The computer program product of claim 16, wherein the at least one computing device is further configured to perform actions including: determining whether the calculated TCR complies with a target TCR; and in response to the calculated TCR not complying with the target TCR: repeating the creating of the TCAD model, the calculating of the resistance versus voltage characteristic, the converting of the resistance versus voltage characteristic, and the calculating of the TCR, wherein the repeated creating of the TCAD model is performed on polysilicon resistor having an adjusted dose level different from the selected dose level.
 18. The computer program product of claim 17, wherein the selected dose level is related to an average polysilicon grain size and wherein the adjusted dose level is related to a greater average polysilicon grain size than the selected dose level.
 19. The computer program product of claim 18, wherein the greater average polysilicon grain size is estimated using the TCAD simulation model.
 20. The computer program product of claim 16, wherein the selected dose level is related to an average polysilicon grain size and wherein the adjusted dose level is related to a lesser average polysilicon grain size than the selected dose level and wherein the lesser average polysilicon grain size is estimated using the TCAD simulation model. 